Abstract

The Monte Carlo method is used to study phase transitions in disordered two-dimensional Potts models in which disorder is realized as nonmagnetic impurities. The temperature dependences of the thermodynamic parameters have been calculated for specific heat C, susceptibility χ, and fourth-order Binder cumulants in the dependence on spin concentration p. The calculations have been performed for the system with periodic boundary conditions. The systems with linear sizes L × L = N, L = 20–160 are considered. The incorporation of nonmagnetic impurities to a spin system is shown to possibly lead to a change of the first-order phase transition to a second-order phase transition. The problem of the universality classes of the critical behavior of low-dimensional diluted systems is discussed.

中文翻译：

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低维无序Potts模型中的相变

摘要

蒙特卡罗方法用于研究无序二维Potts模型中的相变，其中无序被实现为非磁性杂质。对于比热C，磁化率χ和四阶Binder累积量，根据自旋浓度p计算出了热力学参数的温度依赖性。已经针对具有周期性边界条件的系统执行了计算。线性尺寸L × L = N，L的系统= 20–160被考虑。非磁性杂质向自旋系统的掺入显示可能导致一阶相变到二阶相变的变化。讨论了低维稀释系统临界行为的通用性类的问题。